Question

The first term of an AP is 3. The last term of an AP is 83. The sum of all terms is 903. Find number of terms and common difference.

Answer 1

a=3

An=83

Sn=903

Sn=n/2(a+An)

903=n/2(3+83)

n=21

An=a +(n-1)d

83=3+(21-1)d

80=20d

d=4

Answer 2

The number of terms are 21.

The common difference is 4.

Step-by-step explanation:

Given : The first term of an AP is 3. The last term of an AP is 83. The sum of all terms is 903.

To Find : Number of terms and common difference ?

Solution :

The first term of an AP is a=3.

The last term of an AP is l=83.

The sum of all terms is $S_n=903$.

The sum of n terms formula is given by,

$S_n=\frac{n}{2}(a+l)$

$903=\frac{n}{2}(3+83)$

$903=\frac{n}{2}(86)$

$903=43n$

$n=\frac{903}{43}$

$n=21$

The number of terms are 21.

The last term formula of an A.P is

$l=a+(n-1)d$

$83=3+(21-1)d$

$80=20d$

$d=\frac{80}{20}$

$d=4$

The common difference is 4.

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